Let's go back to the original one-liner question, which was concerning a CLUB checkout.
There is no legal requirement for a CLUB checkout. It is a CLUB rule only. One could equally have a club rule stating that all pilots must wear nylon underpants.
Unless the pilot has an expired license or a rating (in which case he cannot be P1 and he has to fly with an instructor), he can legally act as P1.
Therefore he can log it as P1.
More practically, if I can legally act as P1, and I am paying for it, I jolly well WANT to log it
A club checkout doesn't need to be done with an instructor; it can be done with anybody in the P2 seat who reckons himself to be the judge for the day. With a limited company owned aircraft, a Director of the company is a pretty good start.
What have I missed?